Elliptic curve search results

Results (6 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
63.1-a3	63.1-a	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	63.1	\( 3^{2} \cdot 7 \)	\( 3^{4} \cdot 7^{2} \)	$1.33215$	$(-a+2), (-a-2), (a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$1$	$13.02432697$	1.230683220	\( \frac{103823}{63} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}$
63.1-b3	63.1-b	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	63.1	\( 3^{2} \cdot 7 \)	\( 3^{4} \cdot 7^{2} \)	$1.33215$	$(-a+2), (-a-2), (a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$0.373149604$	$14.60752776$	1.030103091	\( \frac{103823}{63} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
441.1-a3	441.1-a	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{4} \cdot 7^{8} \)	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$5.213351238$	1.970461553	\( \frac{103823}{63} \)	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -330 a + 873\) , \( -1537 a + 4066\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-330a+873\right){x}-1537a+4066$
441.1-f3	441.1-f	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{4} \cdot 7^{8} \)	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$5.213351238$	1.970461553	\( \frac{103823}{63} \)	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -330 a + 873\) , \( 1537 a - 4068\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-330a+873\right){x}+1537a-4068$
567.1-c3	567.1-c	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	567.1	\( 3^{4} \cdot 7 \)	\( 3^{16} \cdot 7^{2} \)	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1.319254411$	$4.341442324$	4.329558047	\( \frac{103823}{63} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+9{x}$
567.1-l3	567.1-l	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	567.1	\( 3^{4} \cdot 7 \)	\( 3^{16} \cdot 7^{2} \)	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1$	$4.869175922$	1.840375511	\( \frac{103823}{63} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.